Method of determining a minimum pulse width for a short pulse laser system

ABSTRACT

A method is provided for determining a minimum pulse width for a pulsed laser beam in a short pulse laser system, such that the minimum pulse width accounts for dispersion associated with the pulse laser beam passing through a diffractive optical element. The method includes: determining size data for an ablation to be formed in a surface of a workpiece; determining an operating wavelength for a pulsed laser beam; determining spot size data for the beam incident on the workpiece; determining tolerance data for the spot size of the incident beam; and determining a minimum pulse width for the pulsed laser beam based on the size data for the ablation, the operating wavelength for the laser beam, the spot size data for the laser beam and the tolerance data for the spot size.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication Serial No. 60/398,486 which was filed on Jul. 25, 2002 andis incorporated by reference herein.

FIELD OF THE INVENTION

[0002] The present invention relates to short pulse laser system, andmore particularly, to a method for determining a minimum pulse width fora pulsed laser beam in a short pulse laser system.

BACKGROUND OF THE INVENTION

[0003] Ultrafast lasers generate intense laser pulses with durationsfrom roughly 10−11 seconds (10 picoseconds) to 10−14 seconds (10femtoseconds). A wide variety of potential applications for ultrafastlasers in medicine, chemistry, and communications are being developedand implemented. These lasers are also a useful tool for milling ordrilling holes in a wide range of materials. Hole sizes as small as afew microns, even sub-microns, can readily be drilled. High aspect ratioholes can be drilled in hard materials, such as cooling channels inturbine blades, nozzles in ink-jet printers, or via holes in printedcircuit boards.

[0004] Laser drilling of holes in a particular pattern using opticalparallel processing has been used for a variety of fast and ultrafastlaser applications, and is generally applied using projection imaging ofa mask containing the pattern (usually at a magnification), or abeamsplitter, such as a diffractive optical element (diffractive opticalelement). Optical parallel processing is desirable in order to enablemass production techniques to increase throughput and quickly createcustomer-specified geometries in final products. These geometries oftenrequire multiple small holes to be drilled in a particular pattern thatmust be accurate, consistent, and repeatable from workpiece (thematerial the laser is drilling) to workpiece.

[0005] Parallel processing using a beam splitter usually has theadvantage over mask projection imaging that it has high lightutilization efficiency, hence higher drilling speed. However, there arespecial challenges to using a diffractive optical element in ultrashortlaser processing applications. Ultrashort laser pulses have much largerspectral bandwidth compared long pulses, i.e., they contain manywavelength components, and the diffractive optical element is spectrallydispersive, i.e. different wavelengths are diffracted in differentdirections. It is necessary to understand the behavior and limitationsof using a diffractive optical element in ultrashort laser processing inorder to select the correct laser for the parallel processing system.

[0006] Consequently, in a market that measures its annual revenue inmillions of dollars, the company that develops new methods of makinglaser micromachining tools more accurate and efficient will help tooptimize performance and minimize production cost in a wide variety ofapplications within the laser micromachining industry.

SUMMARY OF THE INVENTION

[0007] In accordance with the present invention, a method is providedfor determining a minimum pulse width for a pulsed laser beam in a shortpulse laser system, such that the minimum pulse width accounts fordispersion associated with the pulse laser beam passing through adiffractive optical element. The method includes: determining size datafor an ablation to be formed in a surface of a workpiece; determining anoperating wavelength for a pulsed laser beam; determining spot size datafor the beam incident on the workpiece; determining tolerance data forthe spot size of the incident beam; and determining a minimum pulsewidth for the pulsed laser beam based on the size data for the ablation,the operating wavelength for the laser beam, the spot size data for thelaser beam and the tolerance data for the spot size.

[0008] Further areas of applicability of the present invention willbecome apparent from the detailed description provided hereinafter. Itshould be understood that the detailed description and specificexamples, while indicating the preferred embodiment of the invention,are intended for purposes of illustration only and are not intended tolimit the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a diagram illustrating optical paths of multiple laserbeams in an exemplary short pulse laser system;

[0010]FIG. 2 is a diagram depicting exemplary laser beam intensityspectrum of two optical pulses;

[0011]FIG. 3 is a diagram illustrating the periodic phase structure of adiffractive optical element;

[0012]FIG. 4 is a flowchart depicting an exemplary method fordetermining a minimum pulse width for a pulse laser in accordance withthe present invention; and

[0013]FIG. 5 is a perspective view illustrating the primary componentsof an ink-jet printer; and

[0014]FIG. 6 is a cross-sectional schematic view of an exemplary ink-jethead.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] In general, the present invention is directed to a method ofdetermining minimum pulse width for a short pulse laser system. Thisminimum pulse width can be used to control and/or to minimize spectraldispersion, thereby making short pulse laser drilling more efficient.While the following description is provided with reference to theparticular application of using picosecond lasers to drill holes forlaser inkjet nozzles, it is readily understood that the broader aspectsof the present invention are generally applicable to short pulse laserapplications.

[0016]FIG. 1 provides a partial view 100 of a short pulse laser systemincluding the following elements: a diffractive optical element 105; anentrance pupil 110; a scan lens 115; a focal plane 120; several rays 125a-f, which form diffraction angles θ1 and θ2; an optical input 130; anoptical axis 132; and a workpiece 135. Distance X and F are alsoindicated in FIG. 1.

[0017] Diffractive optical element 105 is preferably a beamsplitter thatmay be used in applications such as drilling multiple holes in inkjetnozzle workpiece materials. In the present application, a picosecondlaser system, which is a relatively low energy laser, generates opticalinput 130 along optical axis 132, using conventional short pulse lasertechnology. Optical input 130 passes through diffractive optical element105 and is split into a plurality of beams 125 at the point of entrancepupil 110. Diffraction angles θ1 and θ2, are the angles formed by ray125 a and ray 125 d, ray 125 b and ray 125 e, and ray 125 c and ray 125f, respectively, as they pass through scan lens 115.

[0018] Scan lens (also known as an f-theta lens) 115 may be atelecentric scan lens, which maintains the perpendicularity required ofrays 125 a through 125 f with focal plane 120, and is conventionallyknown in laser technology. Scan lenses, and specifically telecentriclenses are commercially available from various vendors, includingRodenstock Precision Optics, and Special Optics. One example of such ascan lens from Special Optics has the following specification:wavelength 1.053 μm, focal length 100 mm, entrance pupil diameter 15 mm,and scan field 30 mm.

[0019] Focal plane 120 is the location where rays 125 a through 125 fare focused after passing through scan lens 115, and thus is the optimallocation to position workpiece 135. F is the focal length of the scanlens, and is further discussed below. X is the distance between opticalaxis 132 and the point where the highest order beam meets focal plane120, and is discussed further below.

[0020] In operation, optical input 130 is generated by a short pulse(picosecond) laser. Incident beam 130 is incident upon diffractiveoptical element 105 along optical axis 132, which is positioned in theentrance pupil 110 of scan lens 115, and is split into the patternrequired according to the particular application; for instance, apattern of beams might consist of 304 beams arranged in an 8×48 array.For simplicity of explanation, FIG. 1 has been limited to illustrateonly two beams 131 a and 131 b. Each beam is defined by at least rays,including a central ray and two edge rays. For instance, beam 131 a isdefined by central ray 125 b and two edge rays 125 a and 125 c. In theparticular application of parallel process laser drilling, it isessential for the central ray of each beam to meet the workpiece 135 ata right angle in order to drill parallel holes and still maintain thepattern established by diffractive optical element 105. Telecentric scanlens 115 maintains the perpendicularity required of central rays 125 b,125 e with focal plane 120, where beams 125 a-f drill holes in workpiece135 according to the pattern established by diffractive optical element105.

[0021]FIG. 2 illustrates beam intensity I as a function of wavelength λfor a first optical pulse 305 and a second optical pulse 310. Thecentral wavelength λ_(o) is identical for the two pulses. Because of themathematical relationship between time and bandwidth (specifically,ΔT*Δλ>=constant), a narrow bandwidth Δλ represents a wide pulse in time,and a wide bandwidth Δλ represents a narrow pulse in time. Thisrelationship is well known in the art and can be shown via Fouriertransform calculations. For a pulse that has Gaussian shape in time, thespectrum is also Gaussian in shape. In this case, the minimum product ofpulse width and bandwidth is

ΔT×Δν=0.44,  (1)

[0022] or, if we use the relationship between frequency and wavelengthof light,

λ·ν=c,  (2)

[0023] we have

ΔT×Δλ=0.44×λ² /c,  (3)

[0024] where c is the speed of light. For example, for a laser operatingat λ=1 μm and a pulse width of ΔT=0.1 ps=1×10⁻¹³ sec, the minimumbandwidth Δλ is $\begin{matrix}\begin{matrix}{{\Delta \quad \lambda_{\min}} = {0.44 \times {\lambda^{2}/( {c \times \Delta \quad T} )}}} \\{= {0.44 \times {( {1 \times 10^{- 6}} )^{2}/( {3 \times 10^{8} \times 1 \times 10^{- 13}} )}}} \\{= {{1.5 \times 10^{- 8}\quad m} = {15\quad {{nm}.}}}}\end{matrix} & (4)\end{matrix}$

[0025] On the other hand, if ΔT=10 ps=1×10⁻¹¹ sec, then the minimumbandwidth Δλ becomes $\begin{matrix}\begin{matrix}{{\Delta \quad \lambda_{\min}} = {0.44 \times {\lambda^{2}/( {c \times \Delta \quad T} )}}} \\{= {0.44 \times {( {1 \times 10^{- 6}} )^{2}/( {3 \times 10^{8} \times 1 \times 10^{- 11}} )}}} \\{= {{1.5 \times 10^{- 10}\quad m} = {{0.15}\quad {{nm}.}}}}\end{matrix} & (5)\end{matrix}$

[0026] A short time pulse is preferred because it minimizes excessthermal effects that lead to misshapen and distorted hole shapes;however, it can be seen from this time-bandwidth relationship that theshorter the duration of laser pulse, the larger the bandwidth andtherefore the larger the spectral dispersion of a given pulse.

[0027]FIG. 3 illustrates the periodic phase structure of diffractiveoptical element 105, with four periods shown. In FIG. 3, the horizontalaxis as shown is distance and the vertical axis is phase (or height ofsurface relief structure) in an actual diffractive optical element. Theperiod D determines the minimum diffraction angle, of which alldiffraction angles (orders) are integer multiples. The particular phasestructure within a period determines the properties of the diffractiveoptical element, such as the beam pattern, diffraction efficiency, anduniformity.

[0028] The periodic diffractive optical element is a diffractivegrating, and thus obeys the laws for diffractive gratings. Thediffracted angle for different orders by the diffractive optical elementis given by the diffraction equation:

θ≈sin θ=mλ/D  (6)

[0029] where m is the diffraction order, λ the wavelength, and D thegrating period. The diffraction equation says that the diffractiveoptical element is dispersive: the diffraction angle θ is a linearfunction of wavelength λ for the same diffraction order m.

[0030] Incident beam 130 is diffracted into multiple beams (differentdiffraction orders m) after diffractive optical element 105 according toequation (1). These beams are focused by the f-θ scan lens onto thelens's focal plane at different lateral positions x for differentdiffraction angles θ. The relation between x and q is given by

x=f×θ,  (7)

[0031] Combining Equations (6) and (7), we have

x=f×θ=f·(m/D)λ.  (8)

[0032] From Equation (8), we see that the lateral focus position is alinear function of wavelength for any given diffraction order m.Equation (8) also shows that for a short pulse laser beam with aspectral bandwidth Δλ, the focus is also dispersed proportional to λ:$\begin{matrix}\begin{matrix}{{\Delta \quad x} = {{f( {m/D} )}\Delta \quad \lambda}} \\{= {( {{f \cdot ( {m/D} )}\lambda} ) \times \Delta \quad {\lambda/\lambda}}} \\{= {x\quad \Delta \quad {\lambda/\lambda}}}\end{matrix} & (9)\end{matrix}$

[0033] Equation (9) shows that the focus dispersion is equal to theproduct of the lateral focus position x and the fractional bandwidth ofthe laser pulse Δλ/λ. The focus dispersion Δx can deteriorate the focussignificantly if Δx is not negligible compared to the laser focus spotsize of the drilling system at zero order m=0, (without dispersion).This forms the basis for later analysis.

[0034] Once it is understood how the higher orders from diffractiveoptical element 105, in conjunction with a telecentric scan lens 115 ina short pulse laser system, cause spectral dispersions and negativelyimpact drilling of workpiece 135, then knowledge of the laser system andknown equations relating diffraction angles, such as diffraction anglesθ1 and θ2, central wavelength λo and change in bandwidth Δλ, diffractiveoptical element period D, and pattern size, provide sufficientinformation to calculate minimum pulse width that will still satisfycustomer specifications for a finished laser drilled product.

[0035] In accordance with the present invention, FIG. 4 illustrates anexemplary method 400 of determining pulse width for a short pulse lasersystem. The method generally includes the steps of: obtainingspecifications for the workpiece 410, determining laser spot size 420,determining spot size tolerance 430, and determining a minimum pulsewidth 440.

[0036] First, specifications are obtained at step 410 for the workpieceto be fabricated by laser parallel drilling. In this step, an operator,technician, or automated tool obtains physical specifications for thefinished workpiece 135 regarding the pattern to be drilled. Thespecifications are normally given to the operator by the productdesigner. In the present invention, the important specifications are thehole size to be drilled, tolerances of the hole size variation, and theoverall pattern size on the workpiece. In one example, the holes to bedrilled have a diameter of 20 μm, with a tolerance specification of 20μm+/−1 μm absolute and standard deviation of σ=0.5 μm, and the holes areto be drilled in parallel over a 15 mm transverse dimension.

[0037] Next, the laser spot size is calculated at step 420. In thisstep, an operator, technician, or automated tool determines laser spotsize according to the workpiece specification and the specific opticalpaths and the optical elements affecting the path. This is usually donein combination of calculation and experimental determination. In oneexample, the diameter of the holes to be drilled is 20 μm. The laserspot size is first determined that it must be equal or smaller than 20μm. Through experiments, a spot size diameter of d=10 microns isdetermined to be able to drill 20 μm holes using a trepanning algorithm.

[0038] The laser spot size tolerance is similarly determined at step430. In this step, an operator, technician, or automated tool, combinesthe specifications obtained in step 410 with the laser spot sizedetermined in step 420 to determine an acceptable tolerance or error inthe spot size that can drill holes that meet the holes size tolerance.For fixed pulse energy and drilling algorithm, the hole size depends onthe laser spot size. Using the parallel drilling system discussed inthis present invention, the laser spot size varies across the workpiecepattern as determined in Step 410. Therefore the operator must determinethe drilled hole size variation as a function of laser spot sizevariation. This is done through either calculation or experiment. In theexample cited above, given a pattern size of 20 μm and a laser spot sizeof 10 μm, a tolerance of plus or minus 0.5 μm is determined to beacceptable, which means the laser spot size may vary between 9.5 and10.5 μm.

[0039] Lastly, a minimum pulse width is determined at step 440. In thisstep, an operator, technician, or automated tool, determines a minimumpulse width for the laser drilling system that can achieve thespecifications obtained in step 410. This step is based on equations(1)-(7) described above. Specifically, a single equation to determineminimum pulse width is derived as set forth below. For clarity,variables used in the following equations are defined as follows:λ=wavelength, ν=frequency, c=speed of light, 3×10⁸ meters/second,Δτ=pulse width, λ_(o)=central operating wavelength, Δλ=bandwidth,d_(o)=spot size diameter, Δd=spot size tolerance, and X_(max)=patternsize (roughly the radius of pattern to be drilled).

[0040] The following analysis uses the assumption of equation (1) andits equivalent equation (3). This assumption depends upon the spectralpurity of the pulse. Thus, it is assumed the temporal shape of the laserpulse is Gaussian. As will be apparent to one skilled in the art, thespectral purity of the laser pulse must be tested for a given lasersystem to ensure the calculations are accurate.

[0041] First, equation (3) is solved for pulse width Δτ as follows:$\begin{matrix}{{\Delta \quad \tau} = {\frac{0.44 \times \lambda}{c}( \frac{\lambda}{\Delta \quad \lambda} )}} & (10)\end{matrix}$

[0042] Once the relationship for Δτ has been determined, a separateequation is developed to relate spot size d, tolerance Δd with bandwidthand central wavelength, taking into consideration of the dispersion ofthe diffractive optical element.

[0043] Referring to FIG. 1, a collimated incident beam 130 strikesdiffractive optical element 105, one of the diffracted beam emergingfrom the diffractive optical element is focused by scan lens 115 ontothe scan lens' focal plane at at lateral position x. If the incidentbeam 130 has a bandwidth Δλ=0, i.e., truly monochromatic, then thediffracted will have the minimum focus spot size determined by theoptical beam delivery system in the absence of the spectral dispersion,in our example, d₀=10 μm. Conversely, if the bandwidth of incident beam130 is not zero, then the effect on the focus spot of the diffractiveoptical element's dispersion must be considered. According to Equation(6), there is a lateral spread of focus position Δx around x.Subsequently, the focus spot size becomes a convolution between theoriginal spot size d₀ and the spread due to dispersion. In the case of aGaussian spatial spot and a Gaussian spectral distribution as discussedin the above example, the convolved focus spot size is given by:$\begin{matrix}{d = \sqrt{d_{0}^{2} + {\Delta \quad x^{2}}}} & (11)\end{matrix}$

[0044] Substituting Δx from equation (9) for maximum Δx, $\begin{matrix}{d_{\max} = \sqrt{d_{0}^{2} + ( {x_{\max}\Delta \quad {\lambda/\lambda}} )^{2}}} & (12)\end{matrix}$

[0045] This equation can be rearranged to solve for the ratio ofbandwidth to central wavelength as follows: $\begin{matrix}{\frac{\Delta \quad \lambda}{\lambda_{0}} = {\frac{1}{x_{\max}}\sqrt{d_{\max}^{2} - d_{0}^{2}}}} & (13)\end{matrix}$

[0046] Lastly, inserting equation (13) into equation (10) provides a wayto determine a minimum pulse width according to specification of thelaser system and the pattern to be drilled.

[0047] As an example, suppose d₀=10 μm, the maximum allowable spot sizeis d_(max)=d₀+Δd=10+0.5=10.5 μm, and the pattern size is x_(max)=10mm=10⁴ μm. In addition, suppose that λ₀=1 μm=10⁻⁴ cm, then we obtain$\frac{\Delta \quad \lambda}{\lambda_{0}} = {{\frac{1}{10^{4}}\sqrt{10.5^{2} - 10^{2}}} = {3.2 \times 10^{- 4}}}$

[0048] Equation (10) above then gives the minimum pulse width that cansatisfy the above condition: $\begin{matrix}{{\Delta \quad \tau} = {{\frac{0.44 \times 10^{- 4}\quad {cm}}{3 \times 10^{10}\quad {cm}\text{/}s}( \frac{1}{3.2 \times 10^{- 4}} )} = {{4.6 \times 10^{- 12}\quad s} = {4.6\quad {ps}}}}} & (13)\end{matrix}$

[0049] As shown by the pulse width equation (13) above, method 400provides a way to determine a minimum pulse width that is withintolerances of pattern and shape specifications. Note that the precedingmethod may also be easily reconfigured to determine a maximum patternsize X_(max) for a given laser system and pulse width.

[0050] A laser drilling system of the present invention may be used toconstruct a nozzle plate of an ink-jet head as further described below.Referring to FIG. 5, an ink-jet printer 1140 includes an ink-jet head1141 capable of recording on a recording medium 1142 via a pressuregenerator. The ink-jet head 1141 is mounted on a carriage 1144 capableof reciprocating movement along a carriage shaft 1143.

[0051] In operation, ink droplets emitted from the ink-jet head 1141 aredeposited on the recording medium 1142, such as a sheet of copy paper.The ink-jet head 1141 is structured such that it can reciprocate in aprimary scanning direction X in parallel with the carriage shaft 1143;whereas the recording medium 1142 is timely conveyed by rollers 1145 ina secondary scanning direction Y.

[0052]FIG. 6 further illustrates the construction of an exemplaryink-jet head 1141. The ink-jet head is primarily comprised of a pressuregenerator 1104 and a nozzle plate 1114. In this embodiment, the pressuregenerator 1104 is a piezoelectric system having an upper electrode 1101,a piezoelectric element 1102, and a lower electrode 1103. Although apiezoelectric system is presently preferred, it is envisioned that othertypes of systems (e.g., a thermal-based system) may also be employed bythe ink-jet head 1141.

[0053] The nozzle plate 1114 is further comprised of a nozzle substrate1112 and a water repellent layer 1113. The nozzle substrate 1112 may beconstructed from a metal or resin material; whereas the water repellantlayer 1113 is made of fluororesin or silicone resin material. In thisexemplary embodiment, the nozzle substrate 1112 is made of stainlesssteel having a thickness of 50 um and the water repellent layer 1113 ismade of a fluororesin having a thickness of 0.1 um.

[0054] The ink-jet head 1141 further includes an ink supplying passage1109, a pressure chamber 1105, and an ink passage 1111 disposed betweenthe pressure generator 1104 and the nozzle plate 1114. In operation, inkdroplets 1120 are ejected from the nozzle 110. The nozzle 1110 ispreferably formed without flash and foreign matter (e.g., carbon, etc.)in the nozzle plate. In addition, the accuracy of the nozzle outletdiameter is 20 um±1.5 um.

[0055] The description of the invention is merely exemplary in natureand, thus, variations that do not depart from the gist of the inventionare intended to be within the scope of the invention. Such variationsare not to be regarded as a departure from the spirit and scope of theinvention.

1. A method for determining a minimum pulse width for a pulsed laserbeam in a short pulse laser system, such that the minimum pulse widthaccounts for dispersion associated with the pulse laser beam passingthrough a diffractive optical element, comprising: determining size datafor an ablation to be formed in a surface of a workpiece; determining anoperating wavelength for a pulsed laser beam; determining spot size datafor the beam incident on the workpiece; determining tolerance data forthe spot size of the incident beam; and determining a minimum pulsewidth for the pulsed laser beam based on the size data for the ablation,the operating wavelength for the laser beam, the spot size data for thelaser beam and the tolerance data for the spot size.
 2. The method ofclaim 1 wherein the ablation is further defined as a circular hole, suchthat the size data for the ablation is a diameter for the circular hole.3. The method of claim 1 wherein the step of determining a minimum pulsewidth further comprises deriving a first relationship between the spotsize of the incident beam and the tolerance for the spot size whichaccounts for dispersion associated with the diffractive optical elementand using the first relationship to determine the minimum pulse widthfor the pulsed laser beam.
 4. The method of claim 1 wherein the step ofdetermining a minimum pulse width further comprises computing theminimum pulse width in accordance with${\Delta \quad \tau} = {\frac{0.44\quad \lambda}{c}( \frac{X_{\max}}{\sqrt{d_{\max}^{2} - d_{0}^{2}}} )}$

where λ is the operating wavelength, c is the speed of light, x_(max) issize data for the ablation, d_(max) is maximum allowable spot size data,and the d₀ is the spot size data.
 5. The method of claim 1 furthercomprises: generating a pulsed laser beam in accordance with the minimumpulse width; passing the pulsed laser beam through a diffractive opticalelement, thereby separating the pulse laser beam into two or more pulsedlaser beams; and directing the two or more pulsed laser beams onto thesurface of the workpiece, thereby forming two or more ablations in thesurface of the workpiece.
 6. The method of claim 5 wherein the step ofgenerating a pulsed laser beam further comprises using a picosecondlaser source.
 7. The method of claim 5 wherein the step of directing thetwo or more pulsed laser beams further comprises focusing the two ormore laser beams onto the surface of the workpiece using an opticelement, and scanning the two or more laser beams along the surface ofthe workpiece by movably adjusting the optic element, thereby forming apattern ablations in the surface of the workpiece.
 8. A method fordrilling multiple holes using a laser drilling system, comprising:determining a minimum pulse width for a pulse laser beam, such that theminimum pulse width accounts for dispersion associated with the pulselaser beam passing through a diffractive optical element; generating apulsed laser beam in accordance with the minimum pulse width; passingthe pulsed laser beam through the diffractive optical element, therebyseparating the pulse laser beam into two or more laser beams; directingthe two or more laser beams onto a surface of a workpiece, therebydrilling multiple holes into the surface of the workpiece.
 9. The methodof claim 8 wherein the step of determining a minimum pulse width furthercomprises determining size data for a hole to be formed in the surfaceof the workpiece; determining an operating wavelength for the pulsedlaser beam; determining spot size data for the beam incident on theworkpiece; determining tolerance data for the spot size of the incidentbeam; and determining a minimum pulse width for the pulsed laser beambased on the size data for the hole, the operating wavelength for thepulsed laser beam, the spot size data for the laser beam and thetolerance data for the spot size.
 10. The method of claim 9 wherein thestep of determining a minimum pulse width further comprises computingthe minimum pulse width in accordance with${\Delta \quad \tau} = {\frac{0.44\quad \lambda}{c}( \frac{X_{\max}}{\sqrt{d_{\max}^{2} - d_{0}^{2}}} )}$

where λ is the operating wavelength, c is the speed of light, x_(max) issize data for the ablation, d_(max) is maximum allowable spot size data,and the d₀ is the spot size data
 11. The method of claim 8 wherein thestep of generating a pulsed laser beam further comprises using apicosecond laser source.
 12. The method of claim 8 wherein the step ofdirecting the two or more laser beams further comprises focusing the twoor more laser beams onto the surface of the workpiece using atelecentric lens, and scanning the two or more laser beams along thesurface of the workpiece by movably adjusting the telecentric lens,thereby drilling a pattern of holes into the surface of the workpiece.13. A laser drilling system, comprising: a laser subsystem operable toproject a pulsed laser beam towards an exposed surface of a workpiece; adiffractive optical element disposed between the laser subsystem and theworkpiece, the diffractive optical element configured to receive thepulsed laser beam from the laser subsystem and operable to partition thelaser beam into a plurality of laser drilling beams; and a means fordetermining a minimum pulse width for the pulsed laser beam, such thatthe minimum pulse width accounts for dispersion associated with thepulsed laser beam passing though the diffractive optical element. 14.The laser drilling system of claim 13 wherein the means for determininga minimum pulse width further comprises computing the minimum pulsewidth in accordance with${\Delta \quad \tau} = {\frac{0.44\quad \lambda}{c}( \frac{X_{\max}}{\sqrt{d_{\max}^{2} - d_{0}^{2}}} )}$

where λ is an operating wavelength for the pulsed laser beam, c is thespeed of light, x_(max) is size data for ablations formed in the surfaceof the workpiece, d_(max) is maximum allowable spot size data for theablations, and the do is spot size data for the laser drilling beamsincident of the workpiece.
 15. The method of claim 1 wherein theworkpiece is further defined as a nozzle plate for an ink-jet head. 16.The method of claim 8 wherein the workpiece is further defined as anozzle plate for an ink-jet head.
 17. The laser drilling system of claim13 wherein the workpiece is further defined as a nozzle plate for anink-jet head.